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Our future, our universe, and other weighty topics

Saturday, November 23, 2013

Cosmic Fine-Tuning Visualized

The evolution of the cosmos is
determined by initial conditions (such as the initial rate of
expansion and the initial mass of matter), as well as by fifteen or
so numbers called physical constants (such as the speed of the light
and the mass of the electron). We have by now measured these physical
constants with extremely high precision, but we have failed to come
up with any theory explaining why they have their particular values.
One of the most surprising discoveries of modern cosmology is the
realization that the initial conditions and physical constants of the
universe had to be adjusted with exquisite precision if they are to
allow the emergence of conscious observers. This realization is
referred to as the “anthropic principle”...Change the initial
conditions and physical constants ever so slightly, and the universe
would be empty and sterile; we would not be around to discuss it. The
precision of this fine-tuning is nothing short of stunning. The
initial rate of expansion of the universe, to take just one example,
had to have been tweaked to a precision comparable to that of an
archer trying to land an arrow in a 1-square-centimeter target
located on the fringes of the universe, 15 billion light years away!

“Chaos and Harmony” by Trinh Xuan
Thuan, Professor of Astronomy, University of Virginia, p. 235

The phrase cosmic fine-tuning is
nowadays used in a theologically neutral sense to mean the universe's
improbable fitness for life (the term may or may not imply the
existence of a fine-tuner). One of the first books on the anthropic
principle discussed above was Paul Davies' book The Accidental
Universe, which had a cover showing a pair of dice and a galaxy.

But rather than imagining a dice-throwing Las Vegas
crapshooter to visualize the idea of cosmic fine-tuning, we should
perhaps imagine something else in Las Vegas: a slot machine. The
slot machine that we need to imagine is one that has not one row that
must consist of matching symbols for a win, but a slot machine with
multiple rows, each of which must have matching symbols to win the
jackpot. Each row represents one of the conditions for intelligent
life that a successful universe must have. The chance of any one row
having all matching symbols is very low, only about 1 in 1,000,000.
To win the jackpot (which in this case is a universe that has the
right conditions for intelligent life), each of the rows must be
successful, consisting of all matching symbols. There are multiple
possible combinations that allow for success (such as all apples on
the first row, all pears on the second row, and all grapes on the
other rows, or all 7's on the even rows and all oranges on the odd
rows). But still the chance of overall success (each row being
successful) is very, very low. The slot machine would look something
like the slot machine shown below (click on the image to expand it).

Now let's take a look at each of the
rows on this slot machine, and discuss the habitability condition
that the row represents, including a mention of why the chance of the
condition being met is roughly as improbable as the chance of getting
all matching symbols on the row when you pull the red slot machine
lever in the slot machine I have depicted.

The word gravity in the visual refers
to the universal gravitational constant of 6.6 X 10-11 N·(m/kg)2 which defines the degree to which matter
attracts other matter through gravitational attraction. The existence
of intelligent life in our universe requires the gravitational
constant to exist within a narrow range of values. Cosmologists say
that if the gravitational constant had been much greater, the
expansion of the universe would have been stopped by the
gravitational attraction between galaxies, and the universe would
have collapsed in on itself before there was time for life to evolve. If the gravitational constant were much
weaker, there would not have been enough gravitational attraction for
galaxies to form.

Referring to the short-lived stars known as blue
giants (which don't last long enough to support planets where life
evolves), and to the type of stars known as red dwarfs (generally
regarded as being stars not as suitable for Earth-like planets as
yellow stars like our sun), the physicist Paul Davies says on page
73 of The Accidental Universe: “If gravity were very
slightly weaker, or electromagnetism very slightly
stronger (or the electron slightly less massive relative to the
proton), all stars would be red dwarfs. A correspondingly tiny change
the other way, and they would all be blue giants.” So apparently
our universe lucked out with its gravitational level, and this was at
least as lucky or improbable as a row match on the slot machine I
have visualized.

In our universe we have the
remarkable coincidence that the proton (which has a mass 1836 times
greater than an electron) has an electric charge identical to the
charge of an electron, the only difference being that the proton
charge is positive and the electron charge is negative. The charge of
the proton is 1.60217657
×10−19
coulomb,
and the charge of the electron
is −1.60217657
×10−19
coulomb.This
scientific paper is by a scientist who used a molecular beam deflection method to conclude
that the proton charge and the electron charge have a magnitude
differing by less than 5 parts in 10,000,000,000,000,000,000.

The
chemistry on which life depends could not exist if the magnitude of
the charge on the electron did not match the magnitude of the charge
on the proton. It would require only a small difference between the
two to make planets unstable (not surprising because electromagnetism
is a force more than a trillion trillion trillion times greater than
the gravity that holds our planet together).

In his book The Symbiotic Universe, astronomer George Greenstein (a professor emeritus at Amherst College) says this about the equality of the proton and electron charges: "Relatively small things like stones, people, and the like would fly apart if the two charges differed by as little as one part in 100 billion. Large structures like the Earth and the Sun require for their existence a yet more perfect balance of one part in a billion billion."

In any universe
containing life, the electron could have any old charge, as long as
the magnitude of the charge exactly matched the magnitude of the
charge of the proton. The fact that both match exactly is
unexplained by the Standard Model of Physics. So a habitable universe
requires a lucky match of the proton and electron charges, which is
at least as improbable as the likelihood of a match on the “Particle
Charges” row on the slot machine I have depicted.

Entropy can be roughly defined as the
amount of waste mass-energy in a system or universe, energy that is
unavailable for work. Entropy is increased when the stars burns up
their nuclear fuel to radiate energy into space, and it is also
increased when matter gets trapped in black holes. It is a
fundamental law of nature that entropy gradually increases as time
passes, a principle known as the Second Law of Thermodynamics.
Scientists say this law will eventually lead in the incredibly distant future to a “heat death” of
the universe, in which there is no usable energy. We know roughly how
much entropy is now in the universe, and if we “rewind the film”
backward all the way back to the time of the Big Bang, we then have a
universe that begins with very, very little entropy. The diagram
below illustrates the point.

Roger Penrose (one of the most famous
cosmologists) has emphasized the fantastic specialness of the
low-entropy state of the early universe. In the video clip below, he
discusses the issue.

At the end of this brief clip Penrose estimates that the
chance of a random universe having entropy as low as the entropy in the early
universe is some inconceivably small number such as 1 in 10N,
where N is a number greater than the total number of particles in the
observable universe. By comparison with such conclusions, the
“entropy” slot on our cosmic slot machine is very modest,
requiring luck of only about 1 in a million for this condition to be
met. This is probably a great underestimation of the luck actually
required for the initial entropy of a life-bearing universe, but at
least it means we don't have to depict a slot machine with a row
stretching on for many miles.

The expansion rate is the rate at
which an expanding universe expands. Around 1975 cosmologists said
there was a problem called the flatness problem, which is the fact
that in order for the universe to be in its current state the initial
expansion rate of the universe (at the time of the Big Bang) had to
be fine-tuned to about 1 part in 1050.
Then the theory of cosmic inflation was developed, which offered a
mechanism that might explain why the universe had such a suitable
initial expansion rate. But even with such a theory, it is still a
very long shot for a universe to start out with an expansion rate
suitable for habitability.

For one thing, lots of conditions have to
be met for cosmic inflation to occur, and leave us with a universe
like ours; so any inflation theory requires its own type of
fine-tuning – perhaps not as much as 1 part in 1050
but still something on the order needed to win a huge lottery
jackpot. In this paper Cal Tech professor Sean Carroll says, “When perturbations
are taken into account, inflation only occurs in a negligibly small
fraction of cosmological histories,” and then defines this fraction
as a number much less than 1 in 1,000,000,000,000,000,000,000,000.
Princeton professor Paul Steinhardt has recently raised many
objections to the inflation theory in this paper,
claiming that cosmic inflation requires fine-tuning to 15 decimal
places (a 1 in 1,000,000,000,000,000 bit of luck). So without
discounting the possibility that the theory of cosmic inflation is
correct, we can say that with or without inflation, to have a
universe begin by chance with an expansion rate suitable for
intelligent life we need something to happen at least as lucky as
about a 1 in a million long shot, which is about the luck requirement
depicted in my slot machine visual for the “Expansion Rate” row.

Dark energy (basically the same
as the cosmological constant) is one of the great unsolved mysteries
of the universe. It's not simply that we don't know enough about it.
The mystery is that dark energy in our universe is so small, even
though quantum field theory suggests it should be so much larger.
Scientists say that quantum uncertainty should cause an ordinary
vacuum to be teeming with short-lived, fleeting particles called
virtual particles. Those particles should give an ordinary vacuum a
very high energy density. When scientists do the calculations, they
come up with a number indicating that ordinary space should be filled
with a vacuum energy density more than 10100
times greater (more than a million billion trillion quadrillion
quintillion sextillion times greater) than the maximum value
consistent with astronomical observations (a problem known as
the "vacuum catastrophe"). The simplest explanation
is that there is some lucky balancing by which negative contributions
to the vacuum energy density cancel out positive contributions,
resulting in a net value near zero. But such a lucky balancing is
incredibly improbable (far more improbable than the chance that all of
the money you earned in a particular decade matches to the penny, by
coincidence, all the money that you spent or charged in that decade).
Some think it actually required a 1 in 10100
long shot for dark
energy to be so small, but in the “Dark Energy” line of my visual
I merely imagine a requirement that has about a 1 in a million chance
of occurring.

The
size of atoms...is determined by...the mass of the electron. If that
mass were less, atoms would be a lot larger. .. If the mass of the
electron changed just a little bit, we would have things like
'molecules' and 'chemistry', but the specific rules that we know in
the real world would change in important ways...Complicated molecules
like DNA or proteins or living cells would be messed up beyond
repair. To bring it home: Change the mass of the electron just a
little bit, and all life would instantly end.

Besides the luck involved in the electron mass having a suitable value, our universe also had great luck in regard to the neutron mass having a suitable value. Physicist Paul Davies says that if the neutron mass were .998 of its actual value, protons would decay into neutrons, and there would be no atoms at all (The Accidental Universe, page 65). Conversely, if the neutron mass were slightly greater, it would mean there could be no long-lived stars like the sun.

So we can conclude that having electron and neutron masses with values compatible with life
requires good luck on the same order as the luck needed for a match
on the “Particle Masses” row of the slot machine I have
visualized.

After the Big Bang, there was only hydrogen, helium, and a little lithium.
All of the other elements were produced inside of stars. Advanced
life requires lots of carbon, oxygen, and nitrogen. Having a
civilization requires additional elements such as iron. Astronomers
say that some of the elements originated in stars that did not blow
up, and others originated in stars that did blow up in supernova
explosions. A universe must meet many requirements to get all the
needed elements in abundant amounts. For one thing, there has to be
something like the weak nuclear force that exists in our universe,
because that is needed for supernova explosions. Another thing needed
are just the right nuclear resonances, which
have to exist in the right way to assure the abundant production of
carbon and oxygen by stars. In this paper scientists
conclude, “Thus,
even with a minimal change of 0.4% in the strength of the N-N force,
carbon-based life appears to be impossible, since all the stars then
would produce either
almost solely carbon or oxygen, but could not produce both elements.”
So the total luck needed for you to have a universe with a
distribution of elements suitable for the evolution of life (with
abundant carbon and oxygen) would seem to be something like the luck
required to get a match on the “Element Abundances” row of the
slot machine I have visualized.

The two fundamental nuclear forces in our universe are the weak nuclear
force (involved in radioactivity) and the strong nuclear force (which
holds together the nucleus of an atom). The
nucleus of atoms such as carbon consists of neutrons with no charge
and protons with a positive charge. All particles with the same
charge repel each other, particularly when they are very close
together. So if it were not for the strong nuclear force, the nucleus
of an atom such as carbon and oxygen could not exist for more than a
second; the electromagnetic repulsion of the protons would cause the
nucleus to fly apart.

In his book The Accidental Universe
physicist Paul Davies says that if the strong nuclear force were 5
percent weaker, the deuteron (a nucleus consisting of a proton and a
neutron) could not exist, making it “doubtful if stable, long-lived
stars could exist at all.” He also notes that if the strong nuclear
force were 2 percent stronger, a nucleus called a diproton
(consisting of only two protons and no neutrons) would exist, making
it doubtful that “any hydrogen would have survived beyond the hot
primeval phase” near the time of the Big Bang (and also causing all
kinds of problems for the existence of stars like the sun). So it
seems that the strong nuclear force had to exist within a very small
range of values. Since the strong nuclear force is roughly a million
billion trillion trillion times stronger than gravitation, we can
conclude that having the strong nuclear force fall within this narrow
range required luck at least as great as the luck needed for a match
on the “Nuclear Forces” row of the slot machine I have depicted.

--------

By now I have discussed each of the
requirements depicted on my slot machine visual, and how each one
represents a very unlikely long shot or coincidence. What is the
overall probability of all of these eight long shots occurring? The
conditions are all independent requirements, without any causal
relation to each other. If one requirement is met, it does not make
it more likely that another requirement will be met. The rules of
probability indicate that to calculate the likelihood of a set of
independent events occurring, you multiply together the likelihood of
each separate event or condition occurring. The likelihood of success
for each condition is no greater than 1 in a million, so to roughly
calculate the chance of all of the conditions being met, we multiply
1 in a million by itself eight times. This gives us a probability of
1 chance in
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
That is the probability mentioned near the top of my slot machine visual, where
it says, “1 winner every
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
tries!”

If we imagine someone pulling the lever
on this cosmic slot machine, we must imagine him pulling the lever
over and over again for many, many centuries before success is
finally reached, and each row on the machine consists of all the same
symbols. A person pulling the red lever over and over again 24 hours
a day would see one successful row every few days, a row consisting
of all matching symbols (such as all apples). But that would only be one of the eight
successful rows needed to win the jackpot, and it would be
overwhelmingly probable that the same row would be unsuccessful the
next time the person pulled the red lever. The person pulling the red
lever over and over would probably need to pull the lever for many
centuries before he saw that each of the rows consisted of all
matching symbols, and the grand jackpot (a habitable universe) was
won.

In conclusion, there is one sentence
that summarizes what science suggests about the anthropic principle,
cosmic fine-tuning, and also man's place in our vast universe:

You are an ordinary person living on an
ordinary street in an ordinary city or town in an ordinary country on
an ordinary continent on an ordinary planet in an ordinary solar
system in an ordinary galaxy in an ordinary cluster of galaxies in a
very, very special universe.

Copyright Notice

All posts on this blog are authored by Mark Mahin, and are protected by copyright. Copyright 2013-2014 by Mark Mahin. All rights reserved. Any resemblance between any fictional character and any real person is purely coincidental.